A Time-Splitting Spectral Method for the Generalized Zakharov System in Multi-Dimensions

  • Authors:

  • Shi Jin;Chunxiong Zheng

  • Affiliations:

  • Aff1 Aff2;Department of Mathematical Science, Tsinghua University, Beijing, P.R. China 100084

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 2006

Quantified Score

Hi-index 0.01

Visualization

Abstract

The generalized Zakharov system (ZS) couples a dispersive field E (scalar or vectorial) and$$\mathcal{J}$$ nondispersive fields$$\{n_j\}_{j=1}^\mathcal{J}$$ with a propagating speed of$$1/\in_j$$. In this paper, we extend our one-dimensional time-splitting spectral method (TSSP) for the generalized ZS into higher dimension. A main new idea is to reformulate the multi-dimensional wave equations for the nondispersive fields into a first-order system using a change of variable defined in the Fourier space. The proposed scheme TSSP is unconditionally stable, second-order in time and spectrally accurate in space. Moreover, in the subsonic regime, it allows numerical capturing of the subsonic limit without resolving the small parameters$$\in_j$$. Numerical examples confirm these properties of this method